Two intersecting cylindrical shells subjected to internal pressure and external moment are of common occurrence in pressure vessel and piping industry. The highest stress intensity occurring in the vicinity of junction, which is a complex space curve when the diameter ratio d/D increases. As the new process of theoretical solution and design criteria research developed by the authors, the stress analysis based on the theory of thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The thin shell theoretical solution for the main shell with cutout, on which a moment is applied, is obtained by superposing a particular solution on the homogeneous solution. The double trigonometric series solution of cylindrical shell subjected to arbitrary distributed normal and tangential forces based on Timoshenko equation is used for the particular solution and the Xue et al.’s solution, for the homogeneous solution based on the modified Morley equation instead of the Donnell shallow shell equation. The displacement function solution for the nozzle with a nonplanar end is obtained on the basis of the Goldenveizer equation instead of Timoshenko’s. The presented results are in good agreement with those obtained by experiments and by three-dimensional finite element method. The present analytical results are in good agreement with WRC Bulletin 297 when d/D is small. The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 8 and d/Dt/T ≤ 2 successfully.

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